Texture bake doesn't match viewport
Your issue is, you baked only the &quot;diffuse: color&quot;, which is only the raw color that the render engine is supposed to use, in addition to other shading infos, to create the final result. If you want the final result, you need to do another kind of baking.
Now the question is, do you want something static that doesn't react to lights, or do you want to keep your model's surface reactive to its surroundings?
If you want something static, make a &quot;combined&quot; baking. It will bake the final result into one texture file. Be aware though, it really does bake the &quot;final&quot; result. Which includes

little shadows created with the lights bouncing on your bump maps
global illuminations
reflections
subsurface scattering

All will be baked and fixed in stone inside one map and nothing will adapt anymore. It will turn your model into a painted statue.
If however you want to keep your model's material simple yet dynamic as it should to its environment, then you need to basically bake the raw data that should be plugged in a principled shader. Which basically is:

albedo data (raw color without shadows)
metallic data if any
specular
roughness
bump / normal / displacement data

And so on as you need.